Prove2Me

Import context: Poincare/SmoothTest/WeakLimit

Definition
KLSModular_FunctionalInequalities_Poincare_SmoothTest_WeakLimit

by Lazyfill · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

functional-inequalitiesimport-contextklskls-conjecturekls-modularlog-concavemodule-contextpoincare-inequality

This bundle retains the import context of the source module FunctionalInequalities.Poincare.SmoothTest.WeakLimit in the modular KLS dependency graph. It adds no new mathematical declarations. Substantive statements and proofs are represented by separate theorem nodes.

Its direct project prerequisite modules are FunctionalInequalities.Poincare.SmoothTest.Basic and FunctionalInequalities.Analysis.Cutoff.SmoothBall. It also directly imports the external prerequisite modules Mathlib.MeasureTheory.Measure.ProbabilityMeasure, Mathlib.Topology.ContinuousMap.Bounded.Basic, and Mathlib.MeasureTheory.Integral.DominatedConvergence.

Original module imports

import FunctionalInequalities.Poincare.SmoothTest.Basic
import Mathlib.MeasureTheory.Measure.ProbabilityMeasure
import Mathlib.Topology.ContinuousMap.Bounded.Basic
import FunctionalInequalities.Analysis.Cutoff.SmoothBall
import Mathlib.MeasureTheory.Integral.DominatedConvergence

Module navigation

Direct project imports: Poincare/SmoothTest/Basic, Analysis/Cutoff/SmoothBall.

Theorems in source order:

Project result: The KLS conjecture.

Original module · FunctionalInequalities.Poincare.SmoothTest.WeakLimit · Frozen source 408915f.

Definition code
import Definitions.Def_KLSModular_FunctionalInequalities_Poincare_SmoothTest_Basic
import Mathlib.MeasureTheory.Measure.ProbabilityMeasure
import Mathlib.Topology.ContinuousMap.Bounded.Basic
import Definitions.Def_KLSModular_FunctionalInequalities_Analysis_Cutoff_SmoothBall
import Mathlib.MeasureTheory.Integral.DominatedConvergence
Source
Frozen KLS source: https://github.com/human-ai-mathematics/kls-lean/blob/408915fd28eb892a7093fa5df6f6c2699e9de144/formalization/FunctionalInequalities/Poincare/SmoothTest/WeakLimit.lean#L1-L598 (commit 408915fd28eb892a7093fa5df6f6c2699e9de144, module `FunctionalInequalities.Poincare.SmoothTest.WeakLimit`, import-context bundle `KLSModular_FunctionalInequalities_Poincare_SmoothTest_WeakLimit`). The line range identifies the complete original source module; this bundle preserves only its direct import context.

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